After checking fluid level is correct, try this, to see if it improves...
into drive,let car accelerate without any gas(do not touch pedal)to max speed (about 30/35mph).stop,then with 1/3rd gas pedal,accelerate to max speed(do not move foot)stop,then foot hard to floor,upto about 60mph,then stop.then only using a max of 1/3rd gas pedal,drive for about 15miles.you have just reset the drivetrain computer setings....the car is fitted with a computer controlled fuzzy logic gearbox,it will try to make you drive as eco as poss,but if used harshly the gearchange can be harsh up and down.....
if driven gently 4th will engage at 43 mph,with a slight clunk.

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That doesn't sound like a problem, it sounds like it's shifting out of "Overdrive" due to low RPM. That would be normal. If it's more noticeable now than in the past, that's likely just wear of the parts (that's an old transmission at this point), or need transmission fluid checked/replaced. Only someone who knows transmissions can really diagnose if there is any problem, but what you are feeling is the normal downshift out of "overdrive" into the next gear, the only question is is it more noticeable now than in the past.

Since the transmission shifting and torque converter lock (cruise speeds) up are computer controlled you need to have a scanner hooked up that can read Transmission control module (TCM) fault codes. Also check for engine codes as this could be a misfire, but in that case the check engine light should be flashing while the engine is misfiring and set a fault code. If no codes of any kind are present in memory when the testing is done you almost certainly have a mechanical fault in the transmission like a malfunctioning torque converter clutch, but even that should set a fault code, so have the testing done.

2008 Tucson? It should still be under warranty. Does it have more than 100,000 miles on it? Are you the original owner? If not, does it have less than 60,000 miles on it?.. If so, it's still under warranty - take it in to get fixed under warranty.

One possibility is that the speed sensor is going out. When that happens the computer gets bad information and thus makes bad decisions. When the car goes into 2nd all of the solenoids are actually off. That is so if there is some kind of problem the transmission gets no power, then it still has P, R, N, 2nd. It would be kind of weird, maybe, to see only the 1-2 shift being affected but I can't really think of anything else that could cause that kind of problem.